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The central compact object 1E 161348$-$5055 in the supernova remnant RCW 103has a spin period $\sim 6.67$ hr, making it the slowest isolated pulsar. It isbelieved that a supernova fallback disk is required to spin down the neutronstar to the current spin period within a few $10^3$ yr. The mass of thefallback disk around newborn neutron stars can provide useful information onthe supernova processes and the possible detection limit with optical/infraredobservations. However, it is controversial how massive the disk is in the caseof 1E 161348$-$5055. In this work we simulate the spin evolution of a magnetarthat is driven by the interaction between the disk and the star's magneticfield. Compared with previous studies, we take into account various criticalconditions that affect the formation and evolution of the fallback disk. Ourcalculation shows that we can reproduce the extremely slow spin of 1E161348$-$5055 when taking the initial disk mass $M_{\rm d} \sim 10^{-7}M_{\odot}$ and the neutron star magnetic field $B\geq 5 \times 10^{15}$ G. Thisimplies that 1E 161348$-$5055 may be a magnetar with very special initialparameters. However, if future observations reveal more objects like 1E161348$-$5055, then stringent constraints can be obtained on the supernovafallback.

On the fallback disk around the slowest isolated pulsar, 1E 161348$-$5055